Conversations with Britain have improved recently and there was a genuine effort to solve the problems which had emerged after Brexit, according to Minister for Foreign Affairs Simon Coveney.
He said that politicians may need to "surprise people" to resolve the dispute over the protocol and that renewed technical discussions between the UK and the EU this week had gone "reasonably well".
"Political leadership is about making things happen and sometimes surprising people, and I think that's what we need to do over the next few weeks, to provide reassurance," Mr Coveney told reporters at a press conference.
"I think the conversations we're having now with the British government certainly suggest to me that we are in a different space now, one we haven't been in for quite some time, where there is a genuine effort ... on actually how we can solve these problems together.
""I don't think we can get everything agreed in the space of three weeks, that is completely unrealistic. But the question is can we make progress that is measurable and serious in that period where people can see we're on a course that the people can start believing in?"
He said the Government was looking for a "nil-all draw" in negotiations between the UK and the European Union to resolve the row over the Northern Ireland Protocol.
Speaking in London following a meeting of the British-Irish Intergovernmental Conference, he said: "What we're after here is a nil-all draw, where everybody can walk away feeling that they haven't won or lost, but they can live with the outcome."
He also told reporters: "You'll see a lot of engagement over the next few weeks in advance of 28 October."
By then, the Northern Ireland Secretary will technically be forced to call another Assembly election, if power-sharing is not restored.
Earlier, in a joint communique, the British and Irish governments said they are doing everything possible to restore government in Northern Ireland.
Reaffirming commitment to the Good Friday Agreement the statement added: "They agreed on the importance of respecting the Agreement in totality.
"They agreed this is what people in Northern Ireland expect and deserve."
The meeting took place amid signs of a softening of attitudes regarding the protocol.
It follows conciliatory statements recently by Mr Heaton-Harris, who said he had not appreciated the amount of cross border economic connections.
Coveney agrees with Varadkar on 'too strict' protocol
Meanwhile, Mr Coveney said the Tánaiste's comment that the Northern Ireland Protocol is too strict and working without being fully implemented is "stating a fact" and that people are making a lot of similar comments.
Tánaiste Leo Varadkar had conceded the protocol is a "little too strict".
He said the protocol is working despite not being fully implemented, demonstrating there is room for "further flexibility for some changes".
Speaking on RTÉ's Morning Ireland, Mr Coveney said it is clear because of the compromises coming from the EU in recent months that it is willing to look "at more flexibility" than it was at the start of this process.
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"Leo is right on that and I think that is part of the EU messaging," he said.
"We know from the outset it was going to be something difficult to implement."
Mr Coveney said the EU negotiator Maroš Šefčovič has already published a number of papers to show the EU is willing to be a lot more flexible.
"Leo was just stating a fact," said Mr Coveney.
While agreement on changes linked to the protocol remain to be negotiated, the UK, the EU and Ireland have made a noticeable effort in recent days to express a desire for action.
British Foreign Secretary James Cleverly met Mr Coveney in London yesterday, with the pair expressing warm words and a desire for close cooperation on issues including the protocol.
The protocol was agreed by the UK and EU as part of the Withdrawal Agreement and sought to avoid a hard border with Ireland post-Brexit.
But the arrangements have created trade barriers on goods being shipped from Britain to Northern Ireland.
The protocol is vehemently opposed by many unionists in Northern Ireland and the DUP is currently blocking the formation of a power-sharing executive in Belfast in protest.
Stormont collapsed earlier this year amid a row over the protocol and has not returned despite elections in May.
My pleasure to host UK Foreign Secretary @JamesCleverly at the Irish Embassy London for a working dinner. James & I discussed Brexit, the protocol, the war in Ukraine as well as our shared work at the UN Security Council. We agreed to work closely together on all. 🇮🇪🇬🇧 pic.twitter.com/To01YdO6nW— Simon Coveney (@simoncoveney) October 6, 2022
Negotiations between UK and EU officials restarted yesterday afternoon.
Taoiseach Micheál Martin warned "difficulties" exist in reaching an agreement on the protocol but he said there is a "genuine desire" from all sides to do so.
He said space is now needed to allow the UK and the European Union to reach a resolution.
Legislation to enable the UK government to effectively tear up parts of the protocol is to return to Westminster on 11 October.
The Northern Ireland Protocol Bill has already cleared the House of Commons and will be debated at second reading by the House of Lords, which is expected to consider it at length, next week.
Good to meet @Simoncoveney this evening. As our closest neighbour, I am committed to working with Ireland on important issues including energy security and fixing the problems with the Northern Ireland Protocol. pic.twitter.com/gFjYN6PlSA— James Cleverly🇬🇧 (@JamesCleverly) October 6, 2022
Additional reporting: PA, Reuters